Triggerring left click events via python on 3D view screen
You could try casting a ray from a specific angle, and see where on the mesh the ray intersects.

Check the mathutils library for the function intersect_ray_tri

mathutils.geometry.intersect_ray_tri(v1, v2, v3, ray, orig, clip=True)


Blender API intersect_ray_tri Function

Here is some code I found googling:

http://blenderartists.org/forum/archive/index.php/t-154521.html

def CheckIntersections(mesh):
     intersects = 0
     obj = Blender.Object.GetSelected()
     origin = Blender.Mathutils.Vector(obj[0].getLocation("worldspace"))
     ray = Blender.Mathutils.Vector(0,0,20)
     print "Shooting ray from ",origin," towards ",ray
     for f in mesh.faces: # for each face
          v = f.verts # get vertices
          intersectionpoint = Blender.Mathutils.Intersect(v[0].co,v[1].co,v[2].co,ray,origin,1)
          if intersectionpoint != None:
               print "Ray intersects face at ", intersectionpoint
     intersects = intersects + 1


If you know the vertices of the object you want to position the 3D cursor on, you can select those verticies (1 or more) and snap cursor to selected (with more selected, it will go in the center (average) of the selected vertices).